Job Feldbrugge

TL;DR: In this article, the authors propose to deform the contour of integration over metrics into the complex plane, exploiting Picard-Lefschetz theory to transform the path integral from a conditionally convergent integral into an absolutely convergent one.

TL;DR: A new mathematical tool is introduced-Picard-Lefschetz theory-for defining the semiclassical path integral for gravity, and it is proved that primordial tensor (gravitational wave) fluctuations are unsuppressed.

TL;DR: In this article, the authors provide a detailed study of the Lorentzian path integral for quantum gravity in the semiclassical expansion and show a problematic instability is implied by a basic assumption which is the basis of such fundamental aspects as the stability of quantum de Sitter spacetime, the adiabatic vacuum from which inflation is supposed to start, and a smooth semi-classical beginning of the universe.

TL;DR: It is demonstrated that the scale-dependence of the Betti numbers yields a promising measure of cosmological parameters, with a potential to help in determining the nature of dark energy and to probe primordial non-Gaussianities.

TL;DR: In this paper, the authors presented a numerical analysis of the topology of a set of cosmologically interesting 3D Gaussian random fields in terms of their Betti numbers β_0, β_1, and β_2.